FV_n = PV * (e^r_s*N)

r_BD = [D/F] * [360/t]

r_BD = annualized yield on a bank discount basis

D = dollar discount (face value - purchase price)

F = face value of the bill

t = number of days until maturity

EAY = [(1+HPY)^365/t] - 1

HPY = holding period yield

t = number of days until maturity

R_mm = [360*r_BD] / [360-(t*r_BD)]

R_mm = HPY*(360/t)

X = Number of observations / Σ(1/x_i)

*Find what this measures/when it's used

L_y = [(n+1)*y] / 100

y = percentage point at which we are dividing the distribution

L_y = location (L) of the percentile (P_y) in the data set sorted in ascending order

MAD = Σ|x_i-X| / n

n = number of items in the data set

X = mean

| | = absolute value

σ^{2 =} Σ(x_i-μ)² / N

Variances = observation - population mean

σ ⁼ [Σ(x_i-μ)² / N]^1/2

s/X

Sample standard deviation / sample mean

[r_p-r_f] / s_p

(mean portfolio return - risk free return) / standard deviation of portfolio returns

s_k = [n / [(n-1)(n-2)]]  *  [Σ(x_i-X)³ / s³]

As n becomes large, the first term reduces to 1/2

[ [ [n*(n+1)] / [(n-1)(n-2)(n-3)] ] * [(Σ(x_i-X)⁴ / s⁴] ]   -  [ [3(n-1)²] / [(n-2)(n-3)] ]

As n becomes large, the first term becomes 1/n and the third term becomes 3

P(E) = a / (a+b)

Odds of "a" to "b"; switch numerator to b for probability of "b" to "a"

P(A|B) = P(AB) / P(B)

Probability of A given B is the probability of A and B over Probability of B

P(AB) = P(A|B) * P(B)

Probability of A and B is the probability of A given B times the probability of B

P(A|B) = P(A)

P(A or B) = P(A) + P(B) - P(AB)

P(A and B) = P(A) * P(B)

P(A) = P(AS) + P(AS^c)

*Don't know what this is at all

P(A) = P(A|S₁) * P(S₁) + P(A|S₂) * P(S₂) + ...+ P(A|S_n) * P(S_n)

Where set of events s is mutually exclusive and exhaustive

E(X) = Σ P(x_i)*x_i

xi = one of n possible outcomes

1. E(X) = E(X|S)P(S) + E(X|S^c)P(S^c)

2. E(X) = E(X|S₁) * P(S₁) + E(X|S₂) * P(S₂) + ...+ E(X|S_n) * P(S_n)

Where: E(X) = the unconditional expected value of X

E(X|S₁) = the expected value of X given Scenario 1

P(S₁) = the probability of Scenario 1 occurring

The set of events {S₁, S₂,..., S_n} is mutually exclusive and exhaustive.

Cov (XY) = E{[X - E(X)][Y - E(Y)]}

Cov (R_A,R_B) = E{[R_A - E(R_A)][R_B - E(R_B)]}

Corr (R_A,R_B) = Cov (R_A,R_B) / [(σ_A)(σ_B)]

_nC_r = (n over r) = n! / [(n-r)!*(r!)]

Used when the order in which the items assigned the labels is not important

F(x) = n * p(x)

For the nth observation

P(X=x) = _nC_x*(p)^x*(1-p)^n-x

p = probability of success

1-p = probability of failure

nCx = number of possible combinations of having x successes in n trials. Aka number of ways to choose x from n when the order does not matter

90% - x ± 1.65s

95% - x ± 1.96s

99% - x ± 2.58s

Mean ± ...

Approximately 50% of all observations lie in the interval mean ± (2/3)σ

Approximately 68% of all observations lie in the interval mean ± 1σ

Approximately 95% of all observations lie in the interval mean ± 2σ

Approximately 99% of all observations lie in the interval mean ± 3σ

Minimize P(R_pT)

Where:

R_p = portfolio return

R_T = target return

(E(R_p)-R_t) / σ_p

E(R_p) = expected portfolio return

R_t = target return

EAR = e^r_cc - 1

Where:

r_cc = continuously compounded annual rate

HPRt = e^(r_cc*t) - 1

Sampling error of the mean = Sample mean - Population mean

= X - μ

Sample mean ± (reliability factor * standord error)

Reliability factor = The standard normal random variable for which the probability of an observation lying in either tail is α / 2

[(X-μ₀)] / [(s / n^1/2)]

X = sample mean

μ₀ = hypothesized population mean

s = standard deviation of the sample

 n = sample size

M = (V-V_x) * 100

M = momentum oscillator value

V = last closing price

V_x = closing price x days ago (typically 10)

RSI = 100 - [100 / (1+RS)]

RS = sum of up changes for the period / sum of absolute value of down changes for the period

%k = 100*[(C-L14)/(H14-L14)]

C = last closing price

L14 = lowest price in last 14 days

H14 = highest price in last 14 days

%D (signal line) = Average of the last three %K values calculated daily

Change in value / Average value

[Ending value-beginning value] / [(ending value+beginning value) / 2]

Change in Demand / Change in Price

**Not percent

Total Revenue - Total Economic Costs

Total Economic Costs aka explicit + implicit cost

MRP of labor = change in total revenue / change in quantity of labor

Marginal product * Product price (when a firm's in perfect competition)

Profits are maximized when:

(MRP₁ / Price of input 1) = (MRP_n / Price of input n)

Computes the aggregate market share of the N largest firms in the industry.

Ratio will equal 0 for perfect competition and 100 for a monopoly

Adds up the squares of the market shares of each of the largest N companies in the market.

Equals 1 for a monopoly.

Value of goods and services included in GDP measured at current prices

Nominal GDP = quantity produced in Year t * Prices in Year t

Refers to the value of goods included in GDP measured at base-year prices

Real GDP = Quantity produced in Year t * Base-year prices

[Value of current year output at current year prices / value of current year output at base year prices] * 100

[Nominal GDP / Real GDP] * 100

GDP = C + I + G + (X - M)

C = consumer spending on final goods and services

I = gross private domestic investment, which includes business investment in capital goods and changes in inventory

G = government spending on final goods and services

X = exports

M = imports

GDP = consumer spending on goods and services

+ Business gross fixed investment

+ Change in inventories

+ Government spending on goods and services

+ Government gross fixed investment

+ Exports - imports

+ Statistical discrepancy

Sum of incomes received by all factors of production used to generate final output

Employee compensation, corporate and government enterprise profits before taxes, interest income, rent and unincorporated business net income, indirect business taxes less subsidies

Accounts for the wear and tear or depreciation that occurs in capital stock during the production process.

Represents the amount that must be reinvested by the company in the business to maintain current productivity levels

Personal income - personal taxes

aka

Houseold consumption + Household saving

S = I + (G - T) + (X - M)

S is savings? I is investment or income?

Relationship between income and the Real Interest Rate

Disposable income = GDP - Business saving - Net taxes

S - I = (G - T) + (X - M)

MV = PY M/P and Md/P = kY

Where:

k = I/V

M = Nominal money supply

M_d = Nominal money demand

M_d/P is referred to as real money demand and M/P is real money supply

Y = AF(L,K)

Where:

Y = aggregate output

L = quantity of labor

K = quantity of capital

A = technological knowledge or total factor productivity (TFP)

Growth in potential GDP = Growth in technology + W_L(Growth in Labor) + W_K(Growth in Capital)

Growth in per capital potential GDP = Growth in technology + W_K(Growth in capital-labor ratio

ULC = W/O

Where:

O = output per hour per worker

W = total labor compensation per hour per worker

Nominal interest rate (R_N) reflects the real interest rate (R_R) and the expected inflation rate (∏^C)

R_N = R_R + ∏^C

Ignoring taxes:

1/(1-MPC)

Assuming taxes:

1/[1 - MPC(1-t)]

Current Account

Capital Account

Financial Account

S_DC/FC * (P_FC / P_DC)

S_DC/FC = Nominal Spot exchange rate

P_FC = foreign price level (quoted in terms of the foreign currency)

P_DC = Domestic price level (qutoed in terms of the domestic currency)

F_DC/FC = (1 / S_FC/DC) * [(1 + r_DC) / (1 + r_FC)]

or

F_DC/FC = S_DC/FC * [(1 + r_DC) / (1 + r_FC)]

F_t = S_t+1

[(S_{t + 1}) / S] - 1 = % change in S(DC/FC)_t + 1 = (r_DC - r_FC) / (1 + r_FC)

ω_Xε_X + ω_M(ε_M - 1) > 0

Where:

ω_X = Share of exports in total trade

ω_M = Share of imports in total trade

ε_X = Price elasticity of demand for exports

ε_M = Price elasticity of demand for imports

FCFF = NI + NCC + [Int * (1-t)] - FCInv - WCInv

FCFF = CFO + [Int * (1-t)] - FCInv

EI_FIFO = EI_LIFO + LR (aka LIFO Reserve)

COGS_FIFO = COGS_LIFO - (Change in LR during the year)

Sum of discounted cash flows - Initial Cash Outlay

∑[CF_t / (1 + r)^t] - Outlay

Discount rate that equates the cash flows with the initial cash outlay

∑[CF_t / (1 + IRR)^t] = Outlay

WACC = [(w_d)(r_d)(1 - t)] + [(w_p)(r_p)] + [(w_c)(r_c)]

p = preferred stock

c = common equity

d = debt

v_p = D_p/r_p

v = value

D = dividend

r = cost of preferred stock

CAPM

Dividend Discount Model

P₀ = D₁ / [r_c - g]

g = expected constant growth rate of dividends

r_c = required rate of return on common equity

Rearranges to: r_c = [D₁ / P₀] + g

g = [1 - (D/EPS)] * ROE [

1 - (D/EPS)] aka Earnings Retention Rate (1 - div payout ratio)

r_c = R_f + β[E(R_M) - R_F + CRP]

or

Sovereign yield spread * (Annualized SD of equity index / Annualized SD of Sovereign bond market in terms of the developed market currency)

PQ = VQ + F + C

P = Price per unit

Q = Number of units produced and sold

V = Variable cost per unit

F = Fixed operating costs

C = Fixed financial costs

Q_BE = (F + C) / (P - V)

PQ_OBE = PV + F

Q_OBE = F / (P - V)

P = Price per unit

Q = Number of units produced and sold

V = Variable cost per unit

F = Fixed operating costs

[1 + (Discount / (1 - Discount))]^{[365 / Days beyond discount period]} - 1

Not sure if -1 is raised up or not

R = [(P_T + D_T) / P₀] - 1

P_T = Price at end

D_T = Dividends paid

P₀ = Price at the beginning of the period

R = [(1 + R₁)*(1 + R₂)*...*(1 + R_N)] - 1

Rs are sub-period returns

**Return for WHOLE period

R = [[(1 + R₁)*(1 + R₂)*...*(1 + R_N)]^(1/n)] - 1

**ANNUAL return

r_annual = [(1 + r_period)ⁿ] - 1

r = Return on Investment

n = Number of periods in a year

Rp = w₁R₁ + w₂R₂

w = Weight of asset

R = Return on asset

σ² = [Σ(R_t - μ)²] / T

R_t = Return for period t

T = total number of period

u = Mean of T returns

σ² = [Σ(R_t - R)²] / [T - 1]

R = mean return of the sample observations

σ² = sample variance

σ = [[∑(R_t - μ)²] / T]^1/2

For a sample, denominator is T - 1

σ_p^{2 =} ∑wiwjCov(Ri,Rj)

or

σ_p^{2 =} Σw_i²Var(R_i) + Σw_iw_jCov(R_i,R_j)